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We show that these two classes are canonically identical to those of the Lie pair $(T_{\\mathbb{K}} M, F)$. As a consequence, the Atiyah class of a complex manifold $X$ is isomorphic to the Atiyah class of the corresponding DG manifold $(T^{0,1}_X[1],\\bar{\\partial})$. Moreover, if $X$ is a compact K\\\"ahler manifold, then the Todd class of $X$ is also "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1711.11253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-30T06:43:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0dd22e4ced7bffd4f5b6d57703c7affd4966c1f23608c5c44a9ba7c73b855706","abstract_canon_sha256":"32d5fd6f7b39e505e7994352ab5bcc0f4f9ccab4e1712d36025e5f1b363bac96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:22.258407Z","signature_b64":"s/iao9cQiixoS84dbWjoVaQyyiUlL/Ybdcfufy78KTx6FWrXfbA7F70JijiWKKhwjtHLzYog+V4rfDc9V3arDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e99cc390be9d4632cb5ad78b47656db6a49c9fe1996cb01c2a4287b2ea008117","last_reissued_at":"2026-05-18T00:00:22.257738Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:22.257738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Atiyah and Todd classes arising from integrable distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Maosong Xiang, Ping Xu, Zhuo Chen","submitted_at":"2017-11-30T06:43:57Z","abstract_excerpt":"In this paper, we study the Atiyah class and Todd class of the DG manifold $(F[1],d_F)$ corresponding to an integrable distribution $F \\subset T_{\\mathbb{K}} M = TM \\otimes_{\\mathbb{R}} \\mathbb{K}$, where $\\mathbb{K} = \\mathbb{R}$ or $\\mathbb{C}$. We show that these two classes are canonically identical to those of the Lie pair $(T_{\\mathbb{K}} M, F)$. As a consequence, the Atiyah class of a complex manifold $X$ is isomorphic to the Atiyah class of the corresponding DG manifold $(T^{0,1}_X[1],\\bar{\\partial})$. 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